Using terminology that critics say is exaggerated, Ryan said Medicare is "going bankrupt." He accused Mr. Obama of offering no plan for how to cope with projected financial shortfalls, other than calling on unelected bureaucrats to impose cost cuts. Ryan was referring to the Independent Payment Advisory Board, set up in the president's 2010 health-care reform law, the Affordable Care Act (ACA).

"We propose putting 50 million seniors ... in charge of their own health-care decisions," Ryan said in his speech.

Giving seniors a choice of insurance plans, including traditional Medicare, would encourage competition and help hold down the medical inflation rate, he argued.

Ryan's remarks elicited an animated blend of boos and some cheers, sounds that sometimes competed as the congressman from Wisconsin spoke on, unfazed.

Obama addressed the same crowd Friday via satellite. He said the Romney-Ryan approach would undermine a program millions of Americans hold in high regard. "The problem is that insurance companies, once they’re getting vouchers, they’re really good at recruiting the healthier, younger Medicare recipients," Obama argued. "The entire infrastructure of traditional Medicare ends up collapsing, which means that all seniors at some point end up being at the mercy of the insurance companies."

Their dueling visions set the parameters of a battle that will continue between now and Election Day.

The Republican ticket argues that the way to save Medicare is to introduce more competition, and that Obama's path puts the program on a course toward weakness and insolvency. "Time and again, ... he's put his own job security over your retirement security," Ryan said.

The president, in his most recent weekly address to the nation, said he proposes "reforms that will save Medicare money by getting rid of wasteful spending in the health-care system and reining in insurance companies – reforms that won’t touch your guaranteed Medicare benefits."

Both sides agree that Medicare faces a looming shortfall for covering full benefits, as the number of older Americans soars.

The timing of Ryan's speech was especially sensitive, given that Romney has been scrambling this week to overcome bad publicity about remarks to campaign donors that were caught on videotape. He said 47 percent of Americans wouldn't vote for him because they don't pay taxes and are "dependent" on government.

Some seniors took the comment to be aimed in part at them. Retirees may pay no income tax, although they have paid payroll and other taxes during working careers. At the same time, Ryan's speech offered the potential for the campaign to change the subject to substantive policy matters.

The very notion of reforming Medicare or Social Security has long been viewed as a politically dangerous subject for politicians to touch.

Just as Ryan waded head-on into the danger zone Friday, a new Romney campaign ad does so, as well: In it Sen. Marco Rubio (R) of Florida says, "Anyone who is for leaving Medicare like it is, is for letting it go bankrupt." The ad said the program can be saved, but "only if younger Americans accept that our Medicare will be different than our parents' when we retire."

In his speech, Ryan pitched this as the realistic view. "We respect you enough to level with you," he told the audience. He said Romney's aim would be to work out reforms with bipartisan support, and that some Democrats have already embraced the concepts urged by the GOP candidates.

Responding to an audience question, Ryan said the goal is to avoid a public-debt crisis that could emerge for America in coming years, as has occurred in some European nations.

Ryan also addressed Social Security in his speech. He said projected shortfalls in that program can be fixed with a few changes: raising the retirement age modestly and gradually (starting in the 2020s), and holding wealthier seniors to a slower rise in benefits. Citing some Social Security recipients now in poverty, he said benefits for the lowest-income seniors should rise.

The Obama and Ryan remarks also come as the AARP itself faces some negative publicity. In a Wall Street Journal column, Kimberly Strassel said that newly public e-mails from 2009 and 2010 show the AARP cooperating with the Obama White House to get his health insurance reforms passed. The conservative columnist argued that the Obama law "sets the stage for rationing," and that its moves set the AARP's leadership at odds with many of its members.

In a New York Times/CBS poll released this week, 40 percent of Americans say Medicare will need "major changes" to become financially sound, while 36 percent said "minor changes," and others said no change or were unsure.

On Obama's Affordable Care Act, the poll found that 15 percent of Americans would keep the law as is, and 22 percent would like to see it expanded. But 26 percent would like to see the law's mandate on individuals to buy insurance repealed, and another 30 percent want the whole law repealed.